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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 72 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 80 (c) 144 (d) 72
  2. 2.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 171 (b) 342 (c) 31 (d) 174
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 120 (d) 29
  4. 4.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 30 (b) 32 (c) 36 (d) 31
  5. 5.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 154 (d) 153
  6. 6.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3916 (c) 3828 (d) 3872
  7. 7.What is the 32nd term of the AP 17, 22, 27, 32, …? (a) 177 (b) 160 (c) 172 (d) 155
  8. 8.Which term of the AP 20, 22, 24, 26, … is 42? (a) 12th (b) 13th (c) 11th (d) 21st
  9. 9.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 512 (c) 496 (d) 1056
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
  11. 11.Which term of the AP 6, 13, 20, 27, … is 97? (a) 16th (b) 14th (c) 15th (d) 13th
  12. 12.Which term of the AP 8, 11, 14, 17, … is 107? (a) 36th (b) 33rd (c) 34th (d) 35th
  13. 13.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 384 (b) 720 (c) 52 (d) 360
  14. 14.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 174 (c) 348 (d) 20
  15. 15.What is the 22nd term of the AP 8, 13, 18, 23, …? (a) 118 (b) 110 (c) 105 (d) 113
  16. 16.Which term of the AP 12, 21, 30, 39, … is 75? (a) 9th (b) 10th (c) 8th (d) 7th
  17. 17.What is the 11th term of the AP 3, 6, 9, 12, …? (a) 34 (b) 33 (c) 36 (d) 30
  18. 18.What is the 36th term of the AP 9, 13, 17, 21, …? (a) 144 (b) 149 (c) 140 (d) 153
  19. 19.What is the 31st term of the AP 12, 19, 26, 33, …? (a) 210 (b) 229 (c) 222 (d) 217
  20. 20.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2080 (c) 2146 (d) 4290
  21. 21.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 210 (b) 120 (c) 30 (d) 105
  22. 22.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 250 (c) 235 (d) 470
  23. 23.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 231 (c) 242 (d) 253
  24. 24.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 13 (b) 11 (c) 18 (d) 12
  25. 25.What is the 19th term of the AP 13, 22, 31, 40, …? (a) 171 (b) 175 (c) 184 (d) 162
  26. 26.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 105 (d) 121
  27. 27.What is the 29th term of the AP 12, 17, 22, 27, …? (a) 157 (b) 145 (c) 140 (d) 152
  28. 28.What is the 24th term of the AP 2, 10, 18, 26, …? (a) 194 (b) 186 (c) 192 (d) 184
  29. 29.What is the 11th term of the AP 7, 9, 11, 13, …? (a) 29 (b) 20 (c) 22 (d) 27
  30. 30.What is the 36th term of the AP 7, 13, 19, 25, …? (a) 216 (b) 223 (c) 217 (d) 210
  31. 31.What is the 14th term of the AP 18, 27, 36, 45, …? (a) 117 (b) 135 (c) 126 (d) 144
  32. 32.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 120 (b) 138 (c) 35 (d) 240
  33. 33.What is the missing term in the AP 14, 16, ?, 20, 22? (a) 19 (b) 17 (c) 18 (d) 20
  34. 34.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1226 (c) 1225 (d) 1176
  35. 35.Which term of the AP 10, 12, 14, 16, … is 24? (a) 8th (b) 9th (c) 12th (d) 7th
  36. 36.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 486 (b) 51 (c) 243 (d) 270
  37. 37.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 102 (b) 16 (c) 60 (d) 51
  38. 38.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 20 (b) 154 (c) 80 (d) 77
  39. 39.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 130 (b) 65 (c) 17 (d) 70
  40. 40.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 26 (c) 162 (d) 171

Answer key

  1. 72
  2. 171
  3. 225
  4. 31
  5. 153
  6. 3916
  7. 172
  8. 12th
  9. 528
  10. 256
  11. 14th
  12. 34th
  13. 360
  14. 174
  15. 113
  16. 8th
  17. 33
  18. 149
  19. 222
  20. 2145
  21. 105
  22. 235
  23. 253
  24. 12
  25. 175
  26. 120
  27. 152
  28. 186
  29. 27
  30. 217
  31. 135
  32. 120
  33. 18
  34. 1225
  35. 8th
  36. 243
  37. 51
  38. 77
  39. 65
  40. 162

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